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A JKR solution for a ball-in-socket contact geometry as a bi-stable adhesive system
Ist Teil von
Acta mechanica, 2018-07, Vol.229 (7), p.2835-2842
Ort / Verlag
Vienna: Springer Vienna
Erscheinungsjahr
2018
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
In the present note, we start by observing that in the classical JKR theory of adhesion, using the usual Hertzian approximations, the pull-off load grows unbounded when the clearance goes to zero in a conformal “ball-in-socket” geometry. To consider the case of the conforming geometry, we use a recent rigorous general extension of the original JKR energetic derivation, which requires only adhesionless solutions, and an approximate adhesionless solution given in the literature. We find that depending on a single governing parameter of the problem,
θ
=
Δ
R
/
2
π
w
R
/
E
∗
where
E
∗
is the plane strain elastic modulus of the material couple,
w
the surface energy,
Δ
R
the clearance and
R
the radius of the sphere, the system shows the classical bi-stable behaviour for a single sinusoid or a dimpled surface: pull-off is approximately that of the JKR theory for
θ
>
0.82
only if the system is not “pushed” strong enough, otherwise a “strong adhesion” regime is found. Below this value,
θ
<
0.82
, a strong spontaneous adhesion regime is found similar to “full contact”. From the strong regime, pull-off will require a separate investigation depending on the actual system at hand.